The corresponding contribution to the effective action is given by the Fourier transform of such diagrams, and by summing up this result with the 0PN one, we get the Einstein-Infeld-Hoffmann Lagrangian ([1]}):
\(\mathcal {L}_{EIH}= \frac{m_av_a^2}{2}+\frac{m_av_a^4}{8}+\frac{G_Nm_1m_2}{2r}\biggl [2+3(v_1^2+v_2^2)-7(v_1\cdot v_2)-(v_1\cdot \hat{r})(v_2\cdot \hat{r})-\frac{G_N(m_1+m_2)}{r}\biggr ] \ .\) 
